As already mention in the introduction, there is already a proof of short-time existence due to lmanen, Neves and Schulze [1]}
if the initial network is an irregular tree with bounded curvature. We describe this in a bit more detail.
As we do here, the main issue is to desingularize the higher valence vertices using expanding solitons. They glue
a truncation of a connected regular expanding solition in place of a higher valence vertex, in a ball of radius comparable
to \(\sqrt{t}\)  to obtain an approximation of the flow. They then argue using an expander monotonicity formula which
implies that self-similar expanding flows are “dynamically stable”. The existence of the approximating flow for a positive
time is guaranteed by this monotonicity, which shows that this
approximating flows stays close to the self-similar expanding flows in a suitable neighborhood. The authors establish
that the flow converges to the initial datum only in the sense of varifolds. This makes it difficult to address questions
of uniqueness or multiplicity, as is possible in our approach.
